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# A privet jet flies the same distance in 6 hours that a commercial jet flies in two and a half hours. if the speed of the commercial jet was 75 mph less than thr

A privet jet flies the same distance in 6 hours that a commercial jet flies in two and a half hours. if the speed of the commercial jet was 75 mph less than three times the speed of the private jet, find the speed of each jet.

### 2 Answers by Expert Tutors

Charles S. | Algebra, Geometry, Statistics, AP Calc, GMAT, CFA, ACT, SAT, GRE MathAlgebra, Geometry, Statistics, AP Calc, ...
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I think you have to remember what speed is. Speed is distance over time, which is why it is measured in miles per hour. And most students remember the formula rate = distance / time from middle school. The question gives you info about speeds and times, but not about distance, so once we figure that out, we can get everything else. So if r = d/t then distance = rate * time. We don't know either rate, but we do know they are 75 apart. And we know the distances are the same, so think something like:
distance = speed of commercial * 2.5
and
distance = speed of private * 6

and you know:
speed of commercial = 3*(speed of private) - 75
so you can do one equation that is:
2.5(3r - 75) = 6r (and here r represents the speed of private jet)
Solve for r (I'll leave this part up to you) and you should get something 300 mph for commercial jet and 125 mph for private jet. And, of course, because its almost as fun as six flags, you go back and check your work (125*6) = 750 = 2.5(300) and you go back and read the last sentence of the question to make sure you answer the question asked and don't let your teacher ding you for those 1 or 2 points b/c you didn't answer the question they asked. (Think speed of each jet -- yes I did!)

Kathye P. | Math Geek, passionate about teachingMath Geek, passionate about teaching
5.0 5.0 (150 lesson ratings) (150)
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Hi, Matthew.

This is a "distance" type problem, and you can use the formula d=r*t to solve it, where d is distance, r is rate of speed, and t is time. I am going to use subscripts on the variables to tell them apart, p for private jet and c for commercial jet.

For the private jet, all we know is that the flight took 6 hours, so d=r*6  which is dp=6rp.

For the commercial jet, we know the time is 2.5 hours and we know its rate of speed compared to the private jet, so the equation for the commerical jet is dc=(3rp-75)* 2.5
Notice that the rate in this equation is the rate of the private jet, rp

The final piece of the puzzle is that the distance is the same for both jets, dp=dc  so we can set the two quantities equal to each other:

6rp = (3rp-75)* 2.5

Since we have the same variable in both places in the equation, we can leave the subscripts off now to make the equation simpler.

6r = (3r - 75) * 2.5

6r = 2.5(3r - 75)

6r = 7.5r - 187.5
-7.5 r   -7.5r
-1.5r = -187.5

r = 125

r was the rate of speed for the private jet; Evaluate  3(125) - 75   to get the speed of the commercial jet.

Hope this helps!